Geodesic
Conformal deformations of the Riemannian metrics and homogeneous Riemannian spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 2, pp. 271-282.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper we investigate one-dimensional sectional curvatures of Riemannian manifolds, conformal deformations of the Riemannian metrics and the structure of locally conformally homogeneous Riemannian manifolds. We prove that the nonnegativity of the one-dimensional sectional curvature of a homogeneous Riemannian space attracts nonnegativity of the Ricci curvature and we show that the inverse is incorrect with the help of the theorems O. Kowalski-S. Nikčevi'c [K-N], D. Alekseevsky-B. Kimelfeld [A-K]. The criterion for existence of the left-invariant Riemannian metrics of positive one-dimensional sectional curvature on Lie groups is presented. Classification of the conformally deformed homogeneous Riemannian metrics of positive sectional curvature on homogeneous spaces is obtained. The notion of locally conformally homogeneous Riemannian spaces is introduced. It is proved that each such space is either conformally flat or conformally equivalent to a locally homogeneous Riemannian space.
Classification : 53C20, 53C30
Keywords: conformal deformations; Riemannian metrics; homogeneous Riemannian \break spaces 
@article{CMUC_2002__43_2_a6,
     author = {Rodionov, Eugene D. and Slavskii, Viktor V.},
     title = {Conformal deformations of the {Riemannian} metrics and homogeneous {Riemannian} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {271--282},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {2002},
     mrnumber = {1922127},
     zbl = {1090.53039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2002__43_2_a6/}
}
TY  - JOUR
AU  - Rodionov, Eugene D.
AU  - Slavskii, Viktor V.
TI  - Conformal deformations of the Riemannian metrics and homogeneous Riemannian spaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2002
SP  - 271
EP  - 282
VL  - 43
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2002__43_2_a6/
LA  - en
ID  - CMUC_2002__43_2_a6
ER  - 
%0 Journal Article
%A Rodionov, Eugene D.
%A Slavskii, Viktor V.
%T Conformal deformations of the Riemannian metrics and homogeneous Riemannian spaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 2002
%P 271-282
%V 43
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2002__43_2_a6/
%G en
%F CMUC_2002__43_2_a6
Rodionov, Eugene D.; Slavskii, Viktor V. Conformal deformations of the Riemannian metrics and homogeneous Riemannian spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 2, pp. 271-282. http://geodesic.mathdoc.fr/item/CMUC_2002__43_2_a6/